
Journal of Lie Theory 11 (2001), No. 1, 173184 Copyright Heldermann Verlag 2001 Explicit Formulae for Cocycles of Holomorphic Vector Fields with Values in λ Densities Friedrich Wagemann Institut G. Desargues, Université C. Bernard  Lyon 1, 43, Blv. du 11 Novembre 1918, 69622 Villeurbanne, France We give explicit formulae for the generators of H^{2}( Hol (Σ_{r}), F_{λ} (Σ_{r})) in terms of affine and projective connections, Σ_{r} being a compact Riemann surface punctured in r points. This is done using the cocycles which have been evidenced by V. Ovsienko and C. Roger ["Generalizations of Virasoro group and Virasoro algebra through extensions by modules of tensordensities on S^{1}, Indag. Math., N.S. 9 (1998) 277288] and globalizing them by their transformation property. [ Fulltextpdf (178 KB)] 